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A note of the Gorenstein symmetry conjecture (I)

A mix of human-written and AI-generated textHuman understanding: some partsmath.RT — Representation Theory

Contributed by Qiyue Tang ↗

Version 1 / Oct 26, 2026 / CC BY 4.0

Abstract

Over any field, we reduce the Gorenstein symmetry conjecture to an explicit family of endomorphism algebras over a fixed five-dimensional commutative local symmetric algebra.

Provenance statement

The above results are partial results extracted from several lengthy, multi-turn conversations with AI. They have first been compiled into a Note for reference. The text has undergone some polishing and revision, and the content has been subjected to independent adversarial review by AI.

References

  1. M. Auslander, I. Reiten and S. O. Smalø, Representation Theory of Artin Algebras , Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, 1995. doi:10.1017/CBO9780511623608 (https://doi.org/10.1017/CBO9780511623608).DOI
  2. M. Fang and S. Koenig, Endomorphism algebras of generators over symmetric algebras , J. Algebra 332 (2011), 428--433. doi:10.1016/j.jalgebra.2011.02.031 (https://doi.org/10.1016/j.jalgebra.2011.02.031).DOI
  3. Y. Han and Y. Qin, Reducing homological conjectures by nn-recollements , arXiv:1410.3223v2 (https://arxiv.org/abs/1410.3223v2), 2014.arXiv
  4. C. M. Ringel and M. Schmidmeier, Submodule categories of wild representation type , J. Pure Appl. Algebra 205 (2006), no. 2, 412--422. arXiv:math/0409417 (https://arxiv.org/abs/math/0409417).arXiv
  5. Q. Tang, A reduction of the Gorenstein symmetry conjecture to gendo-symmetric algebras , Hexagon preprint 2610.00396v1 (https://hexagonmath.org/2610.00396v1), 2026.hexagon

Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentOct 25, 2026